Question

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Answer 1

Explicație pas cu pas:

graficul funcției "logaritm":

a)

$\frac{1}{4} \leqslant x \leqslant 8 , f(x) = log_{2}(x) \\ f( \frac{1}{4} ) = - 2 \\ f(1) = 0 \\ f(4) = 2 \\f(8) = 3 \\ functie \: crescatoare$

b)

$\frac{1}{9} \leqslant x \leqslant 9 , f(x) = x log_{3}(x) \\ f( \frac{1}{9} ) = - \frac{2}{9} \\ f(1) = 0 \\ f(3) = 3 \\f(9) = 18 \\ functie \: crescatoare$

c)

$\frac{1}{2} \leqslant x \leqslant 4, f(x) = log_{ \frac{1}{2} }(x) \\ f( \frac{1}{2} ) = 1 \\ f(1) = 0 \\ f(2) = - 1 \\ f(4) = - 2 \\ functie \: descrescatoare$

d)

$1 \leqslant x \leqslant 16, f(x) = \sqrt{x} \times log_{2}(x) \\ f(1) = 0 \\f(4) = 4 \\ f(8) = 6 \sqrt{2} \\ f(16) = 16$